Question

A test consists of 20 true or false questions. To get an A, you must answer at least 18 questions correctly. If you guess on each question, what is the probability that you will get an A?

Use the Standard Normal Table to find the indicated probabilities:

a

b

c

d

Answer 1

it is a binomial probability distribution,

and probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

n=20

probbaility of correct answer = 1/2 = 0.05 [there is only two choices out of which only 1 is correct]

P(X≥18) = P(X=18) + P(x=19)+P(x=20)

P ( X =    18   ) = C(   56   ,   18   )*   0.4900   ^   18   *   0.5100   ^   38   =   0.0043

P ( X =    19   ) = C(   56   ,   19   )*   0.4900   ^   19   *   0.5100   ^   37   =   0.0084

P ( X =    20   ) = C(   56   ,   20   )*   0.4900   ^   20   *   0.5100   ^   36   =   0.0148

P(x≥18)=0.0043+0.0084+0.0148 = 0.02755(answer)

P(getting an A) = 0.02755